I understand that Love number is the ratio between the tide raising potential to the actual deformation of the body, however, I'm not sure if there are ways to detect the Love number from observations outside our solar system. If there are ways, I would like to know the basic theory behind it.
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$\begingroup$ Why not? aanda.org/articles/aa/abs/2018/07/aa31775-17/aa31775-17.html .... aanda.org/articles/aa/abs/2019/03/aa34376-18/aa34376-18.html $\endgroup$– Nilay GhoshNov 15, 2021 at 3:26
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In short, the answer is: yes.
This paper provides an example of direct measurement of the tidal deformation of the close-in Jupiter WASP-103b whose quadrupole Love number turned out to be close to that of our own Jupiter.
Another example of the kind is provided in the above comment by Nilay Ghosh.
Also, from observation of the tidal decay of the close-in Jupoter WASP-12b, it was possible to evaluate the value of its quality function $K_2 = k_2/Q$, which value has turned out to be remarkably close to that of our Jupiter, see this work.
